Answer the following.

1. A company is evaluating the impact of a wellness program offered on-site as a means of reducing employee sick days. A total of 8 employees agree to participate in the evaluation which lasts 12 weeks. Their sick days in the 12 months prior to the start of the wellness program and again over the 12 months after the completion of the program are recorded and are shown below. Is there a significant reduction in the number of sick days taken after completing the wellness program? Use the Sign Test at a 5% level of significance.

Complete the table below.

Employee Sick Days Taken in 12 Months Prior to Program Sick Days Taken in 12 Months Following program Difference (Reduction = Prior-After )
Sign
1 8 7 ( ) ( )
2 6 6 ( ) ( )
3 4 5 ( ) ( )
4 12 11 ( ) ( )
5 10 7 ( ) ( )
6 8 4 ( ) ( )
7 6 3 ( ) ( )
8 2 1 ( ) ( )

Alpha= ________
n= ________
Critical value= ________
Smaller of the number of positive or negative signs= ________

Based on comparing the smaller of the number of positive or negative signs to the Critical value which of the following is (are) true?

A. There is statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
B. There is not statistically significant evidence at alpha=0.05 to show that the median difference (reduction) is positive.
C. There are not enough data points to reach a conclusion.
D. The tied value makes the analysis suspect.

2. A small study (n=10) is designed to assess if there is an association between smoking in pregnancy and low birth weight. Low birth weight babies are those born less than 5.5 pounds. The following data represent the birth weights, in pounds, of babies born to mothers who reported smoking in pregnancy and those who did not.

Mother smoked in pregnancy 5.0 4.2 4.8 3.3 3.9
Mother did not smoke during pregnancy 5.1 4.9 5.3 5.4 4.6

Is there a significant difference in birth weights between mother who smoked during pregnancy and those who did not? Apply the Mann Whitney U Test at a 5% level of significance.

Complete the table below.

Total Sample (Ordered Smallest to Largest) Ranks
Mother Smoked in Pregnancy Mother Did Not Smoke in Pregnancy R
a
n
k Smoked Did Not Smoke Smoked Did Not Smoke
5.0
5.1 1 3.3
4.2 4.9 2
4.8 5.3 3
3.3 5.4
4 4.6
3.9 4.6 5
6
7
8
9
10
R1=____ R2=____

 
2. cont.
Alpha= ________
N1= ________
N2= ________
Critical value U= ________
Smaller of U1 and U2 = ________

Based on comparing the Smaller of U1 and U2 to the Critical value which of the following is (are) true?

A. There is significant evidence at alpha=0.05 to show that the populations of birth weights in mothers who smoked in pregnancy and those who did not are not equal.
B. There is not significant evidence at alpha =0.05 to show that the populations of birth weights in mothers who smoked in pregnancy and those who did not are not equal.
C. There are not enough data points to reach a conclusion.
D. The tied value makes the analysis suspect.

 
3. The recommended daily allowance of Vitamin A for children between 1 and 3 years of age is 400 micrograms (mcg). Vitamin A deficiency is linked to a number of adverse health outcomes including poor eyesight, susceptibility to infection, and dry skin. The following are Vitamin A concentrations in children with and without poor eyesight, a history of infection and dry skin.

With poor eyesight, a history 270 420 180 345 390 430
of infection and dry skin.

Free of poor eyesight, a history 450 500 395 380 430
of infection and dry skin.

Is there a significant difference in Vitamin A concentrations between children with and without poor eyesight, a history of infection and dry skin? Apply the Mann Whitney U Test a 5% level of significance.

Complete the table below.

Total Sample (Ordered Smallest to Largest) Ranks
With
infection Free of infection R
a
n
k With
infection Free of infection With
infection Free of infection
270
450 1 180
420 500 2
180 395 3
345 380
4 380
390 430 5
430 6
7
8
10
11
R1=____ R2=____

 
3. cont.
Alpha= ________
N1= ________
N2 = ________
Critical value U= ________
Smaller of U1 and U2 = ________

Based on comparing the Smaller of U1 and U2 to the Critical value which of the following is (are) true?

A. There is statistically significant evidence at α=0.05 to show that the populations of Vitamin A concentrations in children with and without poor eyesight, a history of infection and dry skin are not equal.
B. There is not statistically significant evidence at α=0.05 to show that the populations of Vitamin A concentrations in children with and without poor eyesight, a history of infection and dry skin are not equal.
C. There are not enough data points to reach a conclusion.
D. The tied value makes the analysis suspect.

4. A study is conducted to assess the potential benefits of an ayurvedic treatment to reduce high cholesterol. Seven patients agree to participate in the study. Each has their cholesterol measured at the start of the study and then again after 4 weeks taking a popular herb called arjuna. Assess whether there is there a difference in total cholesterol after taking the herb using the Wilcoxon Signed Rank Test at a 5% level of significance.

Compete the tables below.

Participant Total Cholesterol
Before Treatment Total Cholesterol
After Treatment Difference (Before-After )
1 250 241
2 265 260
3 240 253
4 233 230
5 255 224
6 275 227
7 241 232

Ordered Absolute Values of Differences Ranks Signed Ranks
3
5
9
9
13
31
48
Total=> 28

W+ = 23 and W- = 5 (Recall that the sum of the ranks, ignoring the signs, will always equal n(n+1)/2 = 7(8)/2.

The test statistic = ________
Alpha= ________
n= ________
Critical value= ________
Smaller of the number of positive or negative signs ________
 
4. cont.

Based on comparing the smaller of the number of positive or negative signs to the Critical value which of the following is (are) true?

A. There is statistically significant evidence at alpha=0.05 to show that the median difference is positive.
B. There is not statistically significant evidence at alpha=0.05 to show that the median
difference is positive.
C. There are not enough data points to reach a conclusion.
D. The tied value makes the analysis suspect.



5. An investigator wants to test if there is a difference in endotoxin levels in children who are exposed to endotoxin as a function of their proximity to operating farms. The following are endotoxin levels in units per milligram of dust sampled from children's mattresses, organized by children's proximity to farms.

Within 5 Miles 54 62 78 90 70
5-24.9 Miles 28 42 39 81 65
25-49.9 Miles 37 29 30 50 53
50 Miles or More 36 19 22 28 27
Total Sample (Ordered Smallest to Largest)
< 5 Miles 5-24.9 Miles 25-49.9 Miles 50+ Miles < 5 Miles 5-24.9 Miles 25-49.9 Miles 50+ Miles

Apply the Kruskal Wallis test at a 5% level of significance.

Alpha= ________
df= ________
Critical value= ________
H= ________

Based on comparing H to the critical value to the Critical value which of the following is (are) true?

A. There is significant evidence at alpha=0.05 t o show that the populations of endotoxin levels in children living varying distances from operating farms are not equal.
B. There is not significant evidence at alpha =0.05 to show that the populations of endotoxin levels in children living varying distances from operating farms are not equal.
C. There are not enough data points to reach a conclusion.
D. The tied value makes the analysis suspect.


Total Points for Chapter Problems 6: /15